课程大纲
Algebra
i). Polynomials
Including Fundamental Theorem of Algebra, Euclidean Division, Remainder Theorem, Rational Roots test, Vieta’s Theorem ... and more.
ii). Techniques with variables Including Techniques dealing with sets of equations, fraction of variables, completing of squares, expansion and simpli?cation... and more.
iii). Inequalities Including linear inequalities, quadratic inequalities, modular inequalities, AM -GM ... and more.
Geometry 1
i). Triangles Including the Theorems of areas, Segments, Law of Sines and Cosines, and several centres in Triangles.
ii). Circles Including the Theorems of Angles, Power of a point, and Two classic ?gures: Fact 5 and Radical Axis.
iii). Transformation and rotation.
Geometry 2
i). Polygons
ii). A very important ?gure in solid geometry —-Tetrahedron Explain the relations between lines, planes, angles, spheres in 3 dimensional geometry using one model —-Tetrahedron.
iii). Other 3D ?gures pyramids, cylinders, spheres ... and more.
iv). Past paper
Number Theory
i). Terminology and fundamental theorems of Number Theory Basic Divisibility Rules and Analysis with Odd, even numbers.
ii). Prime factorisation LCM and GCD and Number of Divisors.
iii). Modular Arithmetic Basic rules of Modular Arithmetic, Chinese remainder Theorem.
Combinatorics
i). Sets and Vein’s Diagrams.
ii). Permutation and combination
iii). Balls and Urns
Functions.
i). Linear function, quadratic function, hyperbolic function, trigonometric function, exponential function loga-rithmic function
ii). Inverse function and composite function
iii). Complex Number
Comprehensive
i). Series and Sequences
ii). Classic comprehensive problems
Revision
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